Every edge is shared by three or more faces in a 4-polytope, as seen in this projection of a tesseract.

In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope.<ref>{{#invoke:citation/CS1|citation
|CitationClass=citation
}}.</ref> In a polygon, an edge is a line segment on the boundary,<ref>Weisstein, Eric W. "Polygon Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonEdge.html</ref> and is often called a side. (Thus a segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.) In a polyhedron or more generally a polytope, an edge is a line segment where two two-dimensional faces meet.<ref>Weisstein, Eric W. "Polytope Edge." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolytopeEdge.html</ref>